A137880 - OEIS

%I #19 Jun 07 2021 04:42:30

%S 1,49,225,23409,108241,11282881,52171729,5438325025,25146664929,

%T 2621261378961,12120640323841,1263442546333969,5842123489426225,

%U 608976686071593889,2815891401263116401,293525499243961920321,1357253813285332678849,141478681658903574000625

%N Indices k of perfect squares among 17-gonal numbers A051869(k) = k*(15*k - 13)/2.

%C Corresponding perfect squares are listed in A137878.

%C Note that all a(n) are perfect squares themselves, their square roots are listed in A137881.

%H Matthew House, <a href="/A137880/b137880.txt">Table of n, a(n) for n = 1..746</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,482,-482,-1,1).

%F A051869( a(n) ) = A137878(n); a(n) = A137881(n)^2.

%F From _Max Alekseyev_, Oct 19 2008: (Start)

%F a(n) = 482*a(n-2) - a(n-4) - 208.

%F a(2n) = ( (15 - sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 + sqrt(30))/30 * (11 - 2*sqrt(30))^n )^2.

%F a(2n+1) = ( (15 + sqrt(30))/30 * (11 + 2*sqrt(30))^n + (15 - sqrt(30))/30 * (11 - 2*sqrt(30))^n )^2. (End)

%F a(n) = a(n-1) + 482*a(n-2) - 482*a(n-3) - a(n-4) + a(n-5). - _Matthew House_, Jun 18 2016

%F G.f.: x*(1 + 48*x - 306*x^2 + 48*x^3 + x^4) / ((1-x)*(1 - 22*x + x^2)*(1 + 22*x + x^2)). - _Colin Barker_, Jun 18 2016

%t Rest@ CoefficientList[Series[x (1 + 48 x - 306 x^2 + 48 x^3 + x^4)/((1 - x) (1 - 22 x + x^2) (1 + 22 x + x^2)), {x, 0, 18}], x] (* _Michael De Vlieger_, Jun 18 2016 *)

%o (PARI) Vec(x*(1+48*x-306*x^2+48*x^3+x^4)/((1-x)*(1-22*x+x^2)*(1+22*x+x^2)) + O(x^20)) \\ _Colin Barker_, Jun 18 2016

%Y Cf. A051869 (17-gonal numbers), A137878 (17-gonal numbers that are perfect squares), A137879, A137881.

%K nonn,easy

%O 1,2

%A _Alexander Adamchuk_, Feb 19 2008

%E Edited and extended by _Max Alekseyev_, Oct 19 2008